a) Field of the invention
The present invention relates to a lens system which uses unhomogenous media.
b) Description of the prior art
As a photographic lens system which is used with cameras and so on, there is known, for example, the Gauss type lesns system. This lens system has defects that it is composed of a large number of, i.e., 6 to 7 lens elements and requires a high manufacturing cost, and that is has a large external design.
It is conceivable, for correcting these defects, to use aspherical lens elements. However, the number of the lens elements can hardly be corrected even by using the aspherical lens elements since these lens elements are incapable of correcting Petzval's sum and chromatic aberration though they are effective for correcting spherical aberration, coma, distortion, etc.
In contrast, attempts are made to correct aberrations by adopting the graded refractive index lens elements which have refractive indices varying from portion to portion thereof. Especially, the radial type graded refractive index lens element which has a refractive index distribution in the radial direction can correct the spherical aberration, etc., like the aspherical lens element, and additionally the Petzval's sum and chromatic aberration at the same time.
A lens system using the radial type graded refractive index lens elements is described on pages 993 and later, Vol.21 of the Applied Optics. This lens system is designed so as to correct the aberrations favorably and comprise lens elements in a number smaller than 1/3 of the number of the lens elements arranged in an ordinary lens system composed only of homogenous lens elements, by using the radial graded refractive index lens elements which have a concave shape (thicker at the marginal portion than at the portion on the optical axis), and are made of a medium having a positive refractive index and arranged symmetrically with regard to an aperture stop as illustrated in FIG. 15.
When the distance as measured from the optical axis in the direction perpendicular to the optical axis is represented by y, the refractive index of the lens portion located at the radial distance y is designated by n(y), the refractive index of the lens portion located on the optical axis is denoted by N.sub.0 and the refractive index distribution coefficients are represented by N.sub.1, N.sub.2, . . . , the refractive index distribution of the radial type graded refractive index lens element is expressed by the following formula (A): EQU n(y)=N.sub.0 +N.sub.1 y.sup.2 +N.sub.2 y.sup.4 +. . . (A)
Since the radial type graded refractive index lens element having the refractive index distribution expressed by this formula has the refractive index distribution coefficients which are different dependently on wavelengths, the coefficients representing dispersing power distribution (Abbe's numbers) of the lens element are expressed as follows: ##EQU1## wherein the reference symbols N.sub.id, N.sub.iF and N.sub.iC represent the refractive power distribution coefficients for the d-line, F-line and C-line respectively. V.sub.0 is the same as the Abbe's number of the homogenous glass material. Further, out of v.sub.i 's, v.sub.1 is the coefficient expressing paraxial amount of the chromatic aberration.
According to the literature mentioned above, when a lens system having a fixed focal length is composed of two radial type graded refractive index lens elements, aberrations are corrected as described below:
Aberrations are classified into seven types, i.e., Seidel's five types of aberrations, longitudinal chromatic aberration and lateral chromatic aberration. Out of these aberrations, the curvature of field is corrected by designing the lens elements so as to have a concave shape and selecting a medium having a positive refractive power for the lens elements, the spherical aberration is corrected by selecting adequate values for the refractive index distribution coefficients of the second and higher orders, and the longitudinal chromatic aberration is corrected by selecting an adequate value for the dispersing power distribution coefficient v.sub.1. Further, the astigmatism is corrected by selecting adequate widths for the airspaces reserved between the radial type graded refractive index lens elements and the aperture stop, whereas the rest aberrations, i.e., coma, distortion and lateral chromatic aberration are corrected by arranging the lens elements symmetrically with regard to the aperture stop so that the aberrations produced before the aperture stop are cancelled with those produced after the aperture stop.
Since the longitudinal chromatic aberration is corrected by selecting an adequate value for the dispersing power distribution coefficient v.sub.1 for the glass material, this aberration cannot be corrected favorably unless the value of v.sub.1 is adequately selected.
Now, description will be made on the relationship between values of V.sub.1 and amounts of the chromatic aberration to be produced.
According to the literature mentioned above, the longitudinal chromatic aberration PAC to be produced by the medium is expressed by the following formula (C): EQU PAC.varies..phi.m/V.sub.1 (C)
wherein the reference symbol .phi.m represents the refractive power of the medium.
For convenience of the description that follows, let us classify values of v.sub.1 into the following three regions:
(a) 0&lt;v.sub.1 &lt;v.sub.0 PA1 (b) v.sub.0 &lt;V.sub.1 PA1 (c) v.sub.1 &lt;0
wherein the reference symbol v.sub.0 represents the Abbe's number of the radial type grade refractive index lens element as measured on the optical axis, which ordinarily has a value on the order of 20 to 70.
Within the region (a), v.sub.1 has a small positive value and chromatic aberration is produced remarkably when rays are refracted by the medium. The graded refractive index lens elements currently available are mostly made of media which have Abbe's numbers within this range. Within the region (b), v.sub.1 has a large positive value and chromatic aberration is produced little when rays are refracted by the medium. In order to obtain the lens system described in the literature mentioned above, it is necessary to use a glass material having an Abbe's number within this range (b). It is very difficult to manufacture a lens element which has a large difference in refractive index by using a glass material having an Abbe's number within this range (b). Within the range (C), v.sub.1 has a negative value and chromatic aberration is produced on the side opposite to the normal side.
As is understood from the description made above, it is difficult to correct the longitudinal chromatic aberration by using graded refractive index lens elements which are made of the glass material having a value of v.sub.1 within the region (a) and can be manufactured easily. As a lens system which has longitudinal chromatic aberration corrected favorably by using graded refractive index lens elements made of the glass materials having values of v.sub.1 within the region (a), there is known the lens system disclosed by Japanese Patent Kokai Publication No. Sho 63-124011. This lens system uses two radial type graded refractive index planar lens elements which have different values of v.sub.1 and are cemented to each other. However, this lens system cannot correct the other aberrations simultaneously though it corrects the longitudinal chromatic aberration favorably.